Method and system for setting an acceleration schedule for engine start

ABSTRACT

Herein provided are methods and systems for setting an acceleration schedule for engine start of a gas turbine engine. A rotational acceleration measurement of the engine is obtained after the engine is energized in response to a start request. The rotational acceleration measurement of the engine is compared to a threshold value within an acceleration band having a maximum threshold and a minimum threshold. An acceleration schedule is determined based on a position of the rotational acceleration measurement of the engine in the acceleration band relative to the threshold value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/591,696, filed on May 10, 2017, the contents of which are herebyincorporated by reference.

TECHNICAL FIELD

The present disclosure relates generally to gas turbine engines, andmore particularly to starts and re-starts.

BACKGROUND OF THE ART

Turbine engine start and re-start capabilities may be designed based ona characterization performed across the ground and flight envelopeand/or based on a simulation model. In some embodiments, the start andre-start processes involve two phases: direct fuel flow control andsub-idle acceleration governing. While in the sub-idle accelerationphase, a control system adjusts the fuel flow to maintain a pre-definedacceleration reference. The objective is to ensure that the proper fueland acceleration schedules are identified to efficiently start theengine in all conditions while avoiding undesirable engine behaviour,such as compressor stall, overheating, engine hang, or flameout.

The engine start process may involve conflicting requirements. Forexample, cold engine acceleration requirements may be dictated bycompressor stability, while hot or high speed engine restartacceleration must be high enough to prevent engine flameout. Forsimplicity, fuel and acceleration schedules are sometimes defined as acompromise that results in limiting the aircraft speed for enginerestart or simply not achieving the shortest possible time to idle inall cases.

As such, there is room for improvement.

SUMMARY

In one aspect, there is provided a method for setting an accelerationschedule for engine start of a gas turbine engine. The method comprisesobtaining a rotational acceleration measurement of the engine after theengine is energized in response to a start request; comparing therotational acceleration measurement of the engine to a threshold valuewithin an acceleration band having a maximum threshold and a minimumthreshold; and determining an acceleration schedule based on a positionof the rotational acceleration measurement of the engine in theacceleration band relative to the threshold value.

In another aspect, there is provided a system for setting anacceleration schedule for engine start of a gas turbine engine. Thesystem comprises a processing unit and a non-transitorycomputer-readable memory having stored thereon program instructionsexecutable by the processing unit. The program instructions executableby the processing unit are for obtaining a rotational accelerationmeasurement of the engine after the engine is energized in response to astart request; comparing the rotational acceleration measurement of theengine to a threshold value within an acceleration band having a maximumthreshold and a minimum threshold; and determining an accelerationschedule based on a position of the rotational acceleration measurementof the engine in the acceleration band relative to the threshold value.

In a further aspect, there is provided a computer readable medium havingstored thereon program code executable by a processor for setting a fuelflow schedule for starting a gas turbine engine of an aircraft, theengine having a compressor inlet and a compressor outlet. The programcode comprising instructions for: obtaining a rotational accelerationmeasurement of the engine after the engine is energized in response to astart request; comparing the rotational acceleration measurement of theengine to a threshold value within an acceleration band having a maximumthreshold and a minimum threshold; and determining an accelerationschedule based on a position of the rotational acceleration measurementof the engine in the acceleration band relative to the threshold value.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures in which:

FIG. 1 is a schematic of an example gas turbine engine;

FIG. 2 is a flowchart illustrating an example method for setting anacceleration schedule of the engine of FIG. 1 in accordance with anembodiment;

FIG. 3A is an example graphical representation of rotationalacceleration;

FIG. 3B is an example graphical representation of acceleration bands;and

FIG. 4 is a block diagram of an example engine control system.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION

FIG. 1 illustrates a gas turbine engine 10 for which an accelerationschedule may be set for engine start and/or restart using the methodsand systems described herein. Note that while engine 10 is a turbofanengine, the acceleration schedule setting methods and systems may beapplicable to turboprop, turboshaft, auxiliary power units (APU), andother types of aircraft engines.

Engine 10 generally comprises in serial flow communication: a fan 12through which ambient air is propelled, a compressor section 14 forpressurizing the air, a combustor 16 in which the compressed air ismixed with fuel and ignited for generating an annular stream of hotcombustion gases, and a turbine section 18 for extracting energy fromthe combustion gases. Axis 11 defines an axial direction of the engine10.

With reference to FIG. 2, there is illustrated a flowchart of an examplemethod 200 for setting an acceleration schedule for starting a gasturbine engine, such as engine 10 of FIG. 1. Note that the expressions“engine start” and “starting an engine” are used throughout the presentdisclosure to refer to both engine starts and restarts. The method 200is used to control the acceleration of the engine 10 in accordance withan acceleration schedule during a sub-idle acceleration phase of theengine 10.

Pre-light-off sub-idle engine acceleration is the result of a pluralityof inputs, including but not limited to starter energy, aircraft speedand oil temperature. Starter torque is directly related to starterenergy and results from a pneumatic or electrical source, such as aground cart or a battery. In electrical systems, starter torque varieswith battery depletion. Similarly, inlet ram recovery pressurizes theengine compressor inlet and varies with aircraft speed. The accumulatedpressure going through the engine spools will provide rotational torqueon the engine core, thus affecting the available torque for the enginestart. As such, monitoring the sub-idle acceleration, pre-light-off orslightly post-light-off, and comparing it to predetermined thresholdsallows the sub-idle acceleration schedule to be set to in accordancewith the actual conditions in which the aircraft is operating.

At step 202, a rotational acceleration measurement is obtained after theengine 10 is energized in response to a start request. An engine startrequest is received and method 200 is triggered. Such start request maybe received from an aircraft command system (not illustrated), forexample, as activated by a pilot. In response to the start request, therotational acceleration measurement of the engine 10 is determined. Forexample a rotational speed of the engine 10 may be obtained via a speedsensor. The rotational speed of the engine may be used to determine therotational acceleration measurement. In some embodiments, the rotationalacceleration measurement is obtained between a time when the engine 10is energized and a time when light-off occurs, where light-off refers toignition of the engine 10. In such case, the rotational accelerationmeasurement obtained may be referred to as a pre-light-off rotationalacceleration measurement. Detection of light-off may be done via one ormore sensors (not illustrated) associated with the engine 10. In someembodiment, rotational acceleration measurement is obtained at the timeof light-off or shortly after light-off.

With additional reference to FIG. 3A, an example graphicalrepresentation of a rotational acceleration 302 of the engine 10 isillustrated. In some embodiments, the rotational accelerationmeasurement is taken from a plurality of rotational acceleration valuesmeasured over a period of time. In other embodiments, the rotationalacceleration measurement corresponds to a single rotational accelerationvalue measured at a specific time. For example, in some embodiments, therotational acceleration measurement is a last measured value 304 beforelight-off 306. In other embodiments, the rotational accelerationmeasurement is a peak measured value 308 taken at a peak accelerationtime 310 corresponding to peak acceleration of the engine 10 beforelight-off 306. In some embodiments, the rotational accelerationmeasurement is a peak acceleration value 312 occurring followinglight-off 306. That is, the peak acceleration value 312 occurs aroundlight-off either at the time of light-off or shortly thereafter.Accordingly, a plurality of rotational acceleration measured values maybe obtained and a specific measured value at any suitable point in time,at a specific engine rotational speed and/or at a specific accelerationcondition may be selected as the rotational acceleration measurement.

At step 204, the rotational acceleration measurement of the engine 10 iscompared to an acceleration band having a maximum threshold and aminimum threshold. With additional reference to FIG. 3B, an accelerationband 350 having a maximum threshold 352 and a minimum threshold 354 isillustrated. In the example illustrated, measured values 304 and 308 areboth illustrated with respect to the acceleration band 350. It should beunderstood that only one of the two values 304, 308, is needed, and thata measured value taken from the rotational acceleration 302 other thanmeasured values 304, 308 may also be used.

In accordance with an embodiment, the comparison of the rotationalacceleration measurement to the acceleration band 350 comprisesdetermining a first difference 376 between the rotational accelerationmeasurement 304, 308 and the minimum threshold 354 and a seconddifference 378 between the maximum threshold 352 and the minimumthreshold 354.

The comparison of the rotational acceleration measurement 304, 308 tothe acceleration band 350 may comprise determining a ratio between thefirst difference and the second difference. For example, the ratio maybe defined as follows:

$\begin{matrix}{{Ratio} = \frac{{ACC} - {T\;\min}}{T_{\max} - {T\;\min}}} & (1)\end{matrix}$

In equation (1), T_(max) is the maximum threshold 352, T_(min) is theminimum threshold 354, and ACC is the rotational accelerationmeasurement 304, 308.

In specific and non-limiting examples of implementation where therotational acceleration measurement corresponds to a rotationalacceleration value measured at a specific time, the maximum threshold352 and the minimum threshold 354 may correspond to a single maximumthreshold value and a single minimum threshold value, respectively.Accordingly, a comparison of the rotational acceleration measured valuemay be made to the minimum threshold value and the maximum thresholdvalue.

For example, in the case where the rotational acceleration measurementis the last measured value 304 before light-off 306, the maximumthreshold 352 and minimum threshold 354 may correspond to a maximum lastvalue 362 before light-off 306 and a minimum last value 364 beforelight-off 306, respectively. As such, a comparison between the lastmeasured value 304 before light-off 306 may be done to the maximum lastvalue 362 and the minimum last value 364, respectively. A ratio betweenthe first difference 376 and the second difference 378 may thus bedetermined. By way of a specific and non-limiting example, if the lastmeasured value 304 equals 40 RPM/s, the maximum last value 362 equals 60RPM/s and the minimum last value 364 equals 25 RPM/s, then, the firstdifference 376 equals 15 RPM/s, the second difference equals 35 RPM/sand the ratio is 3/7.

Similarly, in the case where the rotational acceleration measurement isthe peak measured value 308 pre-light-off, the maximum threshold 352 andthe minimum threshold 353 may correspond to a maximum peak value 366pre-light-off and a minimum peak value 368 pre-light-off, respectively.As such, a comparison between the peak measured value 308 may be done tothe maximum peak value 366 and the minimum peak value 368, respectively.For example, a first difference 376 between the peak measured value 308and the minimum peak value 368 may be determined and a second difference378 between the maximum peak value 366 and the minimum peak value 368may be determined. A ratio between the first difference and the seconddifference may then be determined.

The maximum threshold 352 and the minimum threshold 354 may be set toany suitable value. The maximum threshold 352 may correspond to amaximum engine core acceleration of the engine 10 and the minimumthreshold 354 may correspond to a minimum engine core acceleration ofthe engine 10. Both the maximum engine core acceleration and the minimumengine core acceleration may be a function of a charge level of one ormore batteries used to start the engine 10, aircraft speed and/or oiltemperature. In accordance with an embodiment, the maximum engine coreacceleration of the engine 10 may be achieved with a warm engine, with amaximum aircraft speed allowed for an engine re-start under a maximumengine starter torque. The maximum engine starter torque may be achievedwhen the batteries are fully charged. Similarly, in accordance with anembodiment, the minimum engine core acceleration of the engine 10 may beachieved with a static cold soak engine, when using maximum alloweddepleted batteries.

The maximum threshold 352 and the minimum threshold 354 may bepredetermined by measurement(s) and/or simulation(s) of the engine 10.For example, the maximum threshold 352 may be obtained from measuringthe rotational acceleration of the engine 10 under the conditions setfor maximum engine core acceleration. Similarly, the minimum threshold354 may be obtained from measuring the rotational acceleration of theengine 10 under the conditions set for the minimum engine coreacceleration. By way of another example, a physics based simulationmodel may be used to determine maximum threshold 352 and the minimumthreshold 354.

In other embodiments, the ratio may be between a first differencebetween the rotational acceleration measurement and the maximumthreshold and a second difference between the rotational accelerationmeasurement and the minimum threshold.

Referring back to FIG. 2, at step 206, an acceleration schedule isdetermined based on a position of the rotational accelerationmeasurement of the engine 10 in the acceleration band 350.

In accordance with an embodiment, the position of the rotationalacceleration measurement may be used for selecting values for theacceleration schedule between a maximum acceleration schedule and aminimum acceleration schedule by interpolation. The maximum accelerationschedule may comprises values as a function of time for the sub-idleacceleration phase of the engine 10 and the minimum accelerationschedule may comprises values as a function of time for the sub-idleacceleration phase of the engine 10. In other cases, the maximumacceleration schedule may comprises values as a function of enginerotational speed for the sub-idle acceleration phase of the engine 10and the minimum acceleration schedule may comprises values as a functionof engine rotational speed for the sub-idle acceleration phase of theengine 10.

The maximum acceleration schedule may be associated with the maximumthreshold 352 and the minimum acceleration schedule may be associatedwith the minimum threshold 354. For example, the maximum accelerationschedule and the minimum acceleration schedule may be predetermined bymeasurement(s) and/or simulation(s) of the engine 10 during the sub-idleacceleration phase. Accordingly, the maximum acceleration schedule maybe obtained from measuring the rotational acceleration of the engine 10under the conditions set for maximum engine core acceleration during thesub-idle acceleration phase and the minimum acceleration schedule may beobtained from measuring the rotational acceleration of the engine 10under the conditions set for minimum engine core acceleration during thesub-idle acceleration phase.

In accordance with an embodiment, the values selected for theacceleration schedule between the maximum acceleration schedule and theminimum acceleration schedule may be selected proportional to the ratio.For example, the values selected for the acceleration schedule may bedefined as follows:Values=(ACC _(max) −ACC _(min))*R+ACC _(min)  (2)

In equation (2), ACC_(max) corresponds to the values of the maximumacceleration schedule over time, ACC_(min) corresponds to the values ofthe minimum acceleration schedule over time, and R corresponds to theratio as determined in equation (1).

By way of a specific and non-limiting example, if the ratio isdetermined to be ¾, then the values selected for the accelerationschedule may be ¾ of the values between the maximum accelerationschedule and the minimum acceleration schedule.

In accordance with an embodiment, the acceleration schedule isdetermined by comparing the position of the rotational accelerationmeasurement to a threshold value between the maximum accelerationschedule and the minimum acceleration schedule and selecting either themaximum acceleration schedule of the minimum acceleration schedule. Forexample, if the position of the rotational acceleration measurement isbetween the threshold value and the maximum acceleration schedule thenthe maximum acceleration schedule can be selected and if the position ofthe rotational acceleration measurement is between the threshold valueand the minimum acceleration schedule then the minimum accelerationschedule can be selected.

In accordance with an embodiment, the acceleration schedule isdetermined by comparing the position of the rotational accelerationmeasurement to tolerance bands and selecting the acceleration schedulecorresponding to the position within the tolerance bands. For example,the acceleration schedule may be determined by quantizing the rotationalacceleration measurement into one of a plurality of discrete values andselecting a corresponding acceleration schedule associated with thediscrete value of the rotational acceleration measurement.

In accordance with an embodiment, determining the acceleration schedulecomprises adding a delta to a predetermined sub-idle accelerationschedule. The delta may be selected as a function of the position of therotational acceleration measurement of the engine 10 in the accelerationband 350.

Other practical implementations for determining the accelerationschedule may be possible by determining the acceleration schedule as afunction of the rotational acceleration of the engine 10.

In some embodiments, the method 200 further comprises adjusting the fuelflow to the engine in accordance with the acceleration schedule duringsub-idle acceleration. For instance, after light-off 306 of the engine10, a direct fuel flow may be maintained using a predetermined open loopfuel flow schedule until the sub-idle acceleration phase, during whichthe acceleration schedule may then be applied. While in the sub-idleacceleration phase, the fuel flow may be adjusted to maintain anacceleration level in accordance with the acceleration schedule usingclosed loop tracking of the rotational acceleration of engine 10.

The method 200 may be implemented by a control system. With reference toFIG. 4, the control system may be implemented by a computing device 410,comprising a processing unit 412 and a memory 414 which has storedtherein computer-executable instructions 416. The processing unit 412may comprise any suitable devices configured to implement the method 200such that instructions 416, when executed by the computing device 410 orother programmable apparatus, may cause the functions/acts/stepsperformed as part of the method 200 as described herein to be executed.The processing unit 412 may comprise, for example, any type ofgeneral-purpose microprocessor or microcontroller, a digital signalprocessing (DSP) processor, a central processing unit (CPU), anintegrated circuit, a field programmable gate array (FPGA), areconfigurable processor, other suitably programmed or programmablelogic circuits, or any combination thereof.

The memory 414 may comprise any suitable known or other machine-readablestorage medium. The memory 414 may comprise non-transitory computerreadable storage medium, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Thememory 414 may include a suitable combination of any type of computermemory that is located either internally or externally to device, forexample random-access memory (RAM), read-only memory (ROM), compact discread-only memory (CDROM), electro-optical memory, magneto-opticalmemory, erasable programmable read-only memory (EPROM), andelectrically-erasable programmable read-only memory (EEPROM),Ferroelectric RAM (FRAM) or the like. Memory 414 may comprise anystorage means (e.g., devices) suitable for retrievably storingmachine-readable instructions 416 executable by processing unit 412.Note that the control system can be implemented as part of afull-authority digital engine controls (FADEC) or other similar device,including electronic engine control (EEC), engine control unit (EUC),and the like.

The methods and systems for setting an acceleration schedule of a gasturbine engine described herein may be implemented in a high levelprocedural or object oriented programming or scripting language, or acombination thereof, to communicate with or assist in the operation of acomputer system, for example the computing device 410. Alternatively,the methods and systems for setting an acceleration schedule of a gasturbine engine may be implemented in assembly or machine language. Thelanguage may be a compiled or interpreted language. Program code forimplementing the methods and systems for setting an accelerationschedule of a gas turbine engine may be stored on a storage media or adevice, for example a ROM, a magnetic disk, an optical disc, a flashdrive, or any other suitable storage media or device. The program codemay be readable by a general or special-purpose programmable computerfor configuring and operating the computer when the storage media ordevice is read by the computer to perform the procedures describedherein. Embodiments of the methods and systems for setting anacceleration schedule of a gas turbine engine may also be considered tobe implemented by way of a non-transitory computer-readable storagemedium having a computer program stored thereon. The computer programmay comprise computer-readable instructions which cause a computer, ormore specifically the processing unit 412 of the computing device 410,to operate in a specific and predefined manner to perform the functionsdescribed herein, for example those described in the method 200.

Computer-executable instructions may be in many forms, including programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc., that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

The above description is meant to be exemplary only, and one skilled inthe art will recognize that changes may be made to the embodimentsdescribed without departing from the scope of the invention disclosed.Still other modifications which fall within the scope of the presentinvention will be apparent to those skilled in the art, in light of areview of this disclosure.

Various aspects of the methods and systems for setting an accelerationschedule of a gas turbine engine may be used alone, in combination, orin a variety of arrangements not specifically discussed in theembodiments described in the foregoing and is therefore not limited inits application to the details and arrangement of components set forthin the foregoing description or illustrated in the drawings. Forexample, aspects described in one embodiment may be combined in anymanner with aspects described in other embodiments. Although particularembodiments have been shown and described, it will be obvious to thoseskilled in the art that changes and modifications may be made withoutdeparting from this invention in its broader aspects. The scope of thefollowing claims should not be limited by the embodiments set forth inthe examples, but should be given the broadest reasonable interpretationconsistent with the description as a whole.

The invention claimed is:
 1. A method for setting an accelerationschedule for engine start of a gas turbine engine, the methodcomprising: obtaining a rotational acceleration measurement of theengine after the engine is energized in response to a start request;comparing the rotational acceleration measurement of the engine to athreshold value within an acceleration band having a maximum thresholdand a minimum threshold; and determining an acceleration schedule basedon a position of the rotational acceleration measurement of the enginein the acceleration band relative to the threshold value.
 2. The methodof claim 1, wherein determining an acceleration schedule compriseselecting one of a maximum schedule associated with the maximumthreshold and a minimum schedule associated with the minimum thresholdas a function of the position of the rotational acceleration measurementof the engine relative to the threshold value.
 3. The method of claim 1,wherein the maximum threshold has a maximum acceleration scheduleassociated thereto and the minimum threshold has a minimum accelerationschedule associated thereto, and wherein determining the accelerationschedule comprises selecting values for the acceleration schedulebetween the maximum acceleration schedule and the minimum accelerationschedule proportional to the position of the rotational accelerationmeasurement relative to the threshold value.
 4. The method of claim 1,wherein the maximum threshold is a maximum engine core accelerationachieved with a warm engine, with a maximum aircraft speed allowed foran engine re-start under a maximum engine starter torque.
 5. The methodof claim 1, wherein the minimum threshold is a minimum engine coreacceleration achieved with a static cold soak engine, when using amaximum allowed depleted batteries.
 6. The method of claim 1, whereinthe rotational acceleration measurement is a last measured value beforelight-off, and the maximum threshold and minimum threshold correspond toa maximum last measured value before light-off and a minimum lastmeasured value before light-off, respectively.
 7. The method of claim 1,wherein the rotational acceleration measurement is a peak measured valuepre-light-off, and the maximum threshold and minimum thresholdcorrespond to a maximum peak measured value pre-light-off and a minimumpeak measured value pre-light-off.
 8. The method of claim 1, whereindetermining the acceleration schedule comprises adding a delta to apre-determined sub-idle acceleration schedule, the delta selected as afunction of the position of the rotational acceleration measurement ofthe engine in the acceleration band.
 9. A system for setting anacceleration schedule for engine start of a gas turbine engine, thesystem comprising: a processing unit; and a non-transitorycomputer-readable memory having stored thereon program instructionsexecutable by the processing unit for: obtaining a rotationalacceleration measurement of the engine after the engine is energized inresponse to a start request; comparing the rotational accelerationmeasurement of the engine to a threshold value within an accelerationband having a maximum threshold and a minimum threshold; and determiningan acceleration schedule based on a position of the rotationalacceleration measurement of the engine in the acceleration band relativeto the threshold value.
 10. The system of claim 9, wherein determiningan acceleration schedule comprise selecting one of a maximum scheduleassociated with the maximum threshold and a minimum schedule associatedwith the minimum threshold as a function of the position of therotational acceleration measurement of the engine relative to thethreshold value.
 11. The system of claim 9, wherein the maximumthreshold has a maximum acceleration schedule associated thereto and theminimum threshold has a minimum acceleration schedule associatedthereto, and wherein determining the acceleration schedule comprisesselecting values for the acceleration schedule between the maximumacceleration schedule and the minimum acceleration schedule proportionalto the position of the rotational acceleration measurement relative tothe threshold value.
 12. The system of claim 9, wherein the maximumthreshold is a maximum engine core acceleration achieved with a warmengine, with a maximum aircraft speed allowed for an engine re-startunder a maximum engine starter torque.
 13. The system of claim 9,wherein the minimum threshold is a minimum engine core accelerationachieved with a static cold soak engine, when using a maximum alloweddepleted batteries.
 14. The system of claim 9, wherein the rotationalacceleration measurement is a last measured value before light-off, andthe maximum threshold and minimum threshold correspond to a maximum lastmeasured value before light-off and a minimum last measured value beforelight-off, respectively.
 15. The system of claim 9, wherein therotational acceleration measurement is a peak measured valuepre-light-off, and the maximum threshold and minimum thresholdcorrespond to a maximum peak measured value pre-light-off and a minimumpeak measured value pre-light-off.
 16. The system of claim 9, whereindetermining the acceleration schedule comprises adding a delta to apre-determined sub-idle acceleration schedule, the delta selected as afunction of the position of the rotational acceleration measurement ofthe engine in the acceleration band.
 17. A computer readable mediumhaving stored thereon program code executable by a processor for settinga fuel flow schedule for starting a gas turbine engine of an aircraft,the engine having a compressor inlet and a compressor outlet, theprogram code comprising instructions for: obtaining a rotationalacceleration measurement of the engine after the engine is energized inresponse to a start request; comparing the rotational accelerationmeasurement of the engine to a threshold value within an accelerationband having a maximum threshold and a minimum threshold; and determiningan acceleration schedule based on a position of the rotationalacceleration measurement of the engine in the acceleration band relativeto the threshold value.
 18. The computer readable medium of claim 17,wherein determining an acceleration schedule comprise selecting one of amaximum schedule associated with the maximum threshold and a minimumschedule associated with the minimum threshold as a function of theposition of the rotational acceleration measurement of the enginerelative to the threshold value.
 19. The computer readable medium ofclaim 17, wherein the maximum threshold has a maximum accelerationschedule associated thereto and the minimum threshold has a minimumacceleration schedule associated thereto, and wherein determining theacceleration schedule comprises selecting values for the accelerationschedule between the maximum acceleration schedule and the minimumacceleration schedule proportional to the position of the rotationalacceleration measurement relative to the threshold value.
 20. Thecomputer readable medium of claim 17, wherein the maximum threshold is amaximum engine core acceleration achieved with a warm engine, with amaximum aircraft speed allowed for an engine re-start under a maximumengine starter torque, and wherein the minimum threshold is a minimumengine core acceleration achieved with a static cold soak engine, whenusing a maximum allowed depleted batteries.